Abstract
In an earlier paper we considered a power-series expansion of the metric for a rotating field in terms of a parameter and constructed a solution of Einstein's equations to the first few orders in terms of two harmonic functions. We encountered a pair of Poisson-type equations which were apparently insoluble explicitly. The form of the metric considered was the Weyl-Lewis-Papapetrou form. In this paper we consider a power-series expansion of the most general form of a rotating metric and show that one encounters the same two Poisson equations as before. If these equations are insoluble explicitly, as seems likely, then a general solution depending on two harmonic functions cannot exist in closed form.
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References
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Islam, J.N. On the existence of a general rotating solution of Einstein's equations. Gen Relat Gravit 7, 809–815 (1976). https://doi.org/10.1007/BF00778760
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DOI: https://doi.org/10.1007/BF00778760